arXiv subjects

Yu. Vernov

Publications and source records attributed to Yu. Vernov.

4 recordsLinked to original sources

arXiv2008

Test Functions Space in Noncommutative Quantum Field Theory

It is proven that the $\star$-product of field operators implies that the space of test functions in the Wightman approach to noncommutative quantum field theory is one of the Gel'fand-Shilov spaces $S^β$ with $β< 1/2$. This class of test functions smears the noncommutative Wightman functions, which are in this case generalized distributions, sometimes called hyperfunctions. The existence and determination of the class of the test function spaces in NC QFT is important for any rigorous treatment in the Wightman approach.

hep-th↗

arXiv2006

Generalized Haag's Theorem in SO(1,1) and SO(1,3) Invariant Quantum Field Theory

One of the most important results of the axiomatic quantum field theory - generalized Haag's theorem - is proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained: it has been proved that equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and total cross-sections in these theories.

hep-th↗

arXiv2006

Classical Theorems in Noncommutative Quantum Field Theory

Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.

hep-th↗

arXiv2004

Representations of the Heisenberg algebra on holomorphic functions and Krein structures

Representations of CCR algebras in spaces of entire functions are classified on the basis of isomorphisms between the Heisenberg CCR algebra A_H and star algebras of holomorphic operators. To each representations of such algebras, satisfying a regularity and a reality condition, one can associate isomorphisms and inner products so that they become Krein star representations of A_H, with the gauge transformations implemented by a continuous U(1) group of Krein isometries. Conversely, any holomorphic Krein representation of A_H, having the gauge transformations implemented as before and no null subrepresentation, is shown to be contained in a direct sum of the above representations. The analysis is extended to infinite dimensional CCR algebras, under a spectral condition for the implementers of the gauge transformations.

math-ph↗